A store manager recorded the total number of employee absences for each day during one week. What is the mode of the number of employee absences for that week?
- A. 6
- B. 8
- C. 9
- D. 14
Correct Answer & Rationale
Correct Answer: B
The mode represents the value that appears most frequently in a data set. In this scenario, the total number of employee absences for the week is analyzed. Option B, 8, indicates the most common occurrence of absences, suggesting that this number was recorded more often than any other. Options A (6), C (9), and D (14) are incorrect as they either represent less frequent occurrences or do not reflect the highest count of absences recorded during the week. Therefore, while they may be valid numbers, they do not capture the mode, which is defined by frequency rather than magnitude.
The mode represents the value that appears most frequently in a data set. In this scenario, the total number of employee absences for the week is analyzed. Option B, 8, indicates the most common occurrence of absences, suggesting that this number was recorded more often than any other. Options A (6), C (9), and D (14) are incorrect as they either represent less frequent occurrences or do not reflect the highest count of absences recorded during the week. Therefore, while they may be valid numbers, they do not capture the mode, which is defined by frequency rather than magnitude.
Other Related Questions
Solve the equation for x: (2x-3)/5 = x/10
- A. 2
- B. 3
- C. 1\5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).
Factor completely: b^2 + 3b - 4
- A. (b + 4)(b - 1)
- B. (b - 2)(b - 3)
- C. (b + 1)(b + 2)
- D. (b + 3)(b - 1)
Correct Answer & Rationale
Correct Answer: A
To factor the expression \( b^2 + 3b - 4 \), we need two numbers that multiply to \(-4\) (the constant term) and add to \(3\) (the coefficient of \(b\)). The numbers \(4\) and \(-1\) satisfy these conditions, leading to the factors \( (b + 4)(b - 1) \). Option B, \( (b - 2)(b - 3) \), yields \( b^2 - 5b + 6\), which does not match the original expression. Option C, \( (b + 1)(b + 2) \), results in \( b^2 + 3b + 2\), also incorrect due to the wrong sign on the constant term. Option D, \( (b + 3)(b - 1) \), gives \( b^2 + 2b - 3\), which again does not match. Thus, only option A correctly factors the expression.
To factor the expression \( b^2 + 3b - 4 \), we need two numbers that multiply to \(-4\) (the constant term) and add to \(3\) (the coefficient of \(b\)). The numbers \(4\) and \(-1\) satisfy these conditions, leading to the factors \( (b + 4)(b - 1) \). Option B, \( (b - 2)(b - 3) \), yields \( b^2 - 5b + 6\), which does not match the original expression. Option C, \( (b + 1)(b + 2) \), results in \( b^2 + 3b + 2\), also incorrect due to the wrong sign on the constant term. Option D, \( (b + 3)(b - 1) \), gives \( b^2 + 2b - 3\), which again does not match. Thus, only option A correctly factors the expression.
Multiply (5x - 1)(5x - 1)
- A. 25x^2 + 1
- B. 25x^2 - 1
- C. 25x^2 - 2x + 1
- D. 25x^2 - 10x + 1
Correct Answer & Rationale
Correct Answer: D
To find the product of (5x - 1)(5x - 1), we can use the formula for squaring a binomial, which states that (a - b)² = a² - 2ab + b². Here, a = 5x and b = 1. Calculating this gives: - a² = (5x)² = 25x² - 2ab = 2(5x)(1) = 10x - b² = 1² = 1 Thus, the expanded form is 25x² - 10x + 1, matching option D. Option A (25x² + 1) incorrectly omits the linear term. Option B (25x² - 1) miscalculates the constant term. Option C (25x² - 2x + 1) incorrectly computes the coefficient of the x term. Each of these options fails to accurately reflect the multiplication of the binomials.
To find the product of (5x - 1)(5x - 1), we can use the formula for squaring a binomial, which states that (a - b)² = a² - 2ab + b². Here, a = 5x and b = 1. Calculating this gives: - a² = (5x)² = 25x² - 2ab = 2(5x)(1) = 10x - b² = 1² = 1 Thus, the expanded form is 25x² - 10x + 1, matching option D. Option A (25x² + 1) incorrectly omits the linear term. Option B (25x² - 1) miscalculates the constant term. Option C (25x² - 2x + 1) incorrectly computes the coefficient of the x term. Each of these options fails to accurately reflect the multiplication of the binomials.
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A truck driver sees a road sign warning of an 8% road incline. To the nearest tenth of a foot, what will be the change in the truck's vertical position, in feet, during the time it takes the truck's horizontal position to change by 1 mile? (1 mile = 5,280 ft)
Correct Answer & Rationale
Correct Answer: 422.4
To determine the vertical change during a 1-mile horizontal distance on an 8% incline, we calculate the vertical rise using the formula: vertical rise = incline percentage × horizontal distance. Here, 8% as a decimal is 0.08, and the horizontal distance is 5,280 feet. Therefore, the vertical change is 0.08 × 5,280 = 422.4 feet. Other options are incorrect as they either miscalculate the incline percentage or the conversion of miles to feet. For instance, values significantly lower than 422.4 feet suggest a misunderstanding of the incline's impact, while options above this value imply an overestimation of the incline's effect on vertical change.
To determine the vertical change during a 1-mile horizontal distance on an 8% incline, we calculate the vertical rise using the formula: vertical rise = incline percentage × horizontal distance. Here, 8% as a decimal is 0.08, and the horizontal distance is 5,280 feet. Therefore, the vertical change is 0.08 × 5,280 = 422.4 feet. Other options are incorrect as they either miscalculate the incline percentage or the conversion of miles to feet. For instance, values significantly lower than 422.4 feet suggest a misunderstanding of the incline's impact, while options above this value imply an overestimation of the incline's effect on vertical change.